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dc.rights.licenseCC-BY-NC-ND
dc.contributor.advisorZiltener, Dr. F.J.
dc.contributor.authorBrink, C.B. van den
dc.date.accessioned2021-09-06T18:00:16Z
dc.date.available2021-09-06T18:00:16Z
dc.date.issued2019
dc.identifier.urihttps://studenttheses.uu.nl/handle/20.500.12932/786
dc.description.abstractIn this thesis we generalize the Banach-Alaoglu theorem to topological vector spaces. the theorem then states that the polar, which lies in the dual space, of a neighbourhood around zero is weak* compact. We give motivation for the non-triviality of this theorem in this more general case. Later on, we show that the polar is sequentially compact if the space is separable. If our space is normed, then we show that the polar of the unit ball is the closed unit ball in the dual space. Finally, we introduce the notion of nets and we use these to prove the main theorem.
dc.description.sponsorshipUtrecht University
dc.format.extent468577
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.titleThe Banach-Alaoglu theorem for topological vector spaces
dc.type.contentBachelor Thesis
dc.rights.accessrightsOpen Access
dc.subject.keywordsBanach-Alaoglu, Weak*-compactness, topological vector spaces
dc.subject.courseuuMathematical Sciences


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